As far as I can tell, if you're currently on the Material Plane or an Inner Plane and you cast see invisibility, you see everything that's in the Ethereal Plane that's within "line of sight" to you. The general description of the Ethereal Plane from the Basic Rules says that
The Ethereal Plane is a misty, fog-bound dimension that is sometimes described as a great ocean. Its shores, called the Border Ethereal, overlap the Material Plane and the Inner Planes, so that every location on those planes has a corresponding location on the Ethereal Plane. Certain creatures can see into the Border Ethereal, and the see invisibility and true seeing spell grant that ability.
So it specifically calls out that you can see into the Border Ethereal using see invisibility, and the spell itself just says that you can "see into it". I'm certainly making some assumptions here, but my ruling would be that you see the "corresponding" locations in the Ethereal Plane just like you would by looking anywhere else. That is, I don't see anywhere any particular limit to the range. The only difference between seeing things on the plane you're currently on and seeing what's on the matching location in the Ethereal is that "Ethereal creatures and objects appear ghostly and translucent." If you're outside in broad daylight, you could see pretty far, though maybe it becomes harder to pick out something ghostly and translucent from far away. If you're inside, you probably wouldn't see something on the other side of an opaque wall, just because it blocks your view past it.
Certainly I would understand some other DM ruling differently, especially as these details of how the multiverse is put together are designed to be somewhat customized by each DM. (Chapter 2 of the DMG is literally titled "Creating a Multiverse", after all.) But unless there's clearer guidance elsewhere I'm missing, that's the best by-the-book answer I see.
If you're not on the Material Plane or an Inner Plane when you cast see invisibility, you're pretty much on your own for that one. I have no idea what part of the Ethereal Plane you might see, if any.